Magnetic pendulum device capable of continuously swinging based on liquid crystal elastomer fibers and swinging track calculation method

Abstract

The invention relates to the technical field of simple pendulum systems, in particular to a magnetic pendulum device capable of swinging continuously based on liquid crystal elastomer fibers and a swinging track calculation method.The magnetic pendulum device comprises an experimental platform, a simple pendulum support is installed at the top of the experimental platform, and LCE fibers are fixedly connected to one side of the simple pendulum support; the end, away from the simple pendulum support, of the LCE fiber is fixedly connected with a metal pendulum bob, the top of the experiment platform is provided with a metal graduated scale, the top of the metal graduated scale is in sliding connection with a magnet, and a constant illumination area is applied to the balance position of the LCE fiber. The simple pendulum support comprises a base installed on the top of the experiment platform, and the top of the base is fixedly connected with a metal rod. The metal rod is sleeved with a transverse rod, and a threaded rod is installed on one side of the transverse rod. The problems that an existing simple pendulum system is driven by external force, a new continuous swinging implementation method is difficult to provide, and low-power-consumption continuous swinging of a simple pendulum is difficult to achieve through the temperature effect are solved.

Description

Technical Field

[0001] This invention relates to the field of pendulum system technology, specifically to a magnetic pendulum device based on liquid crystal elastomer fibers that can continuously oscillate and a method for calculating the oscillation trajectory. Background Art

[0002] Some traditional simple pendulums are driven by electromagnetic force, while others are driven by a spring like a pendulum. These are external forces, and temperature generates heat, which is a temperature effect. Different from external forces such as magnetism and the gear force of the spring, it provides a new method to achieve continuous swing of the pendulum. The traditional simple pendulum is affected by non-conservative forces such as air resistance and friction. In the absence of external driving force, the pendulum motion will gradually decay and eventually stop, resulting in high energy consumption and difficulty in achieving sustained swing. Summary of the Invention

[0003] In response to the shortcomings of the existing technology, the present invention provides a magnetic pendulum device based on liquid crystal elastomer fibers that can swing continuously and a method for calculating the swing trajectory. It solves the problem that the existing simple pendulum system relies on external force to drive and is difficult to provide a new method for achieving continuous swing. It uses the effect of temperature to achieve low-power continuous swing of the simple pendulum.

[0004] To achieve the above-mentioned objectives, the present invention provides the following technical solutions: a self-sustaining magnetic pendulum device based on liquid crystal elastomer fibers, comprising an experimental platform, a simple pendulum bracket installed on the top of the experimental platform, an LCE fiber fixedly connected to one side of the simple pendulum bracket, a metal pendulum fixedly connected to the end of the LCE fiber away from the simple pendulum bracket, a metal scale installed on the top of the experimental platform, a magnet slidably connected to the top of the metal scale, a constant illumination area applied to the balance point of the LCE fiber, and the constant illumination area is achieved by using either infrared light emitted by an 808nm high-power near-infrared laser or sunlight focused and heated through a magnifying glass.

[0005] Preferably, the LCE fiber is synthesized from anisotropic rod-shaped liquid crystal molecules and stretchable long-chain polymers, and when the temperature rises due to infrared light stimulation, the liquid crystal monomer molecules rotate or phase change to change the configuration, thereby causing the LCE fiber to shrink and deform macroscopically. When there is no infrared light, the LCE fiber will return to its original length.

[0006] Preferably, the pendulum contains two steady states, a gravitational field and a magnetic field, to form a bistable state. The properties of LCE fibers and the magnetic field are used to realize the remote control of the magnetic pendulum device for self-continuous motion.

[0007] Preferably, the simple pendulum bracket includes a base installed on the top of the experimental platform, the top of the base is fixedly connected to a metal rod, the outside of the metal rod is provided with a cross bar, one side of the cross bar is installed with a threaded rod, the outside of the threaded rod is provided with a nut, one end of the LCE fiber is fixed to the threaded rod, and the distance between the cross bar and the base is greater than the length of the LCE fiber.

[0008] Preferably, the top of the crossbar is provided with a circular hole that is compatible with the metal rod, and one side of the crossbar is provided with a bolt that extends movably into the circular hole.

[0009] Preferably, the metal pendulum is a metal ball, and a limiting hole penetrating its center is provided on one side of the metal pendulum, and one end of the LCE fiber moves through the limiting hole.

[0010] Preferably, the size of the metal pendulum is smaller than the size of the magnet, and the magnet is placed on a metal scale at a distance from the center point of the pendulum support to attract the metal pendulum.

[0011] Preferably, two bending frames are fixedly connected to the top of the experimental platform, a limit rod is fixedly connected between the bending frame and the experimental platform, and the outer sleeve of the limit rod is provided with a bending plate for squeezing the metal scale toward the experimental platform.

[0012] Preferably, a spring is fixedly connected between the bending plate and the experimental platform, and the spring is sleeved on the outside of the limiting rod.

[0013] Preferably, a gasket is fixedly connected to the top of the bending plate, a limiting rod moves through the gasket, and a bolt with one end moving through the bending frame is provided at the top of the bending frame.

[0014] A method for calculating the swing trajectory of a magnetic pendulum device includes the following steps: Step 1: Build a model of the magnetic pendulum device and measure its parameters, including the damping coefficient. The mass of the metal pendulum LCE fiber length , the initial length of the LCE fiber , the magnetic force exerted by the magnet on the metal pendulum The lever arm of the magnetic force relative to the LCE fiber oscillation time of the magnetic pendulum magnetic field strength , lighting area This is used to distinguish the different motion states of the magnetic pendulum within and outside the illuminated area; the horizontal distance between the metal pendulum and the magnet. Dimensionless is obtained by dedimensionalization. Shrinkage coefficient After dimensionless transformation, it becomes ; Step 2: Calculate the motion period of the simple pendulum according to the model parameters; Step 3, obtaining the first control equation of the magnetic pendulum device according to the momentum theorem; Step 4: Import Angular velocity representing LCE fibers , the first control equation is optimized to obtain the second control equation of the magnetic pendulum device, is the angle between the LCE fiber and the vertical direction; Step 5: Calculate the following dimensionless parameters based on the model parameters: ; Where, is the damping coefficient, It is the mass of the metal pendulum. is the length of the LCE fiber, is the initial length of the LCE fiber, is the magnetic force exerted by the magnet on the metal pendulum, It is the lever arm of the magnetic force relative to the LCE fiber. is the acceleration due to gravity, is the swing time of the magnetic pendulum, It is the magnetic field strength. is the horizontal distance between the metal pendulum and the magnet, which is dimensionless after de-dimensionalization. , is the contraction coefficient, which is dimensionless. ; Step six: replace the model parameters in the second control equation with dimensionless parameters to obtain the third control equation that includes both the illuminated interval and the non-illuminated interval.

[0015] Preferably, in step three, the expression of the first control equation of the magnetic pendulum device is: ; Where, is the tangential component of the air damping torque.

[0016] Preferably, in step 4, the expression of the second control equation of the magnetic pendulum device is: ; Where, represents the angular acceleration of the LCE fiber , Represents the radial velocity of the metal pendulum. .

[0017] Preferably, in step six, the expression of the third control equation of the illumination interval is: ; Where, This represents the dimensionless form of the angular velocity of LCE fibers within the illumination range.

[0018] Preferably, in step six, the expression of the third control equation in the non-illumination interval is: ; Where, This represents the dimensionless form of the angular velocity of LCE fibers in the non-illuminated region.

[0019] Compared with the prior art, the present invention provides a magnetic pendulum device based on liquid crystal elastomer fibers that can self-sustainably swing and a method for calculating the swing trajectory, which has the following beneficial effects: 1. By setting up LCE fibers, metal pendulums, magnets and a constant light area, the heat from the light in the constant area is used to continuously drive the simple pendulum system to swing continuously with low power consumption. Instead of relying on external forces such as electromagnetic force and springs, the low-power continuous swing of the simple pendulum is achieved by the temperature provided by the light area, providing a new method for achieving continuous swing.

[0020] 2. The height of the pendulum system can be adjusted as needed by the pendulum support, which can accommodate pendulums composed of LCE fibers of different lengths.

[0021] 3. By setting the bending plate and bolt 2, the metal scale is squeezed and fixed on the experimental platform, which can increase the firmness of the connection between the metal scale and the experimental platform, prevent the magnet from dragging the metal scale along the experimental platform, and at the same time use the gravity of the magnet itself and the magnetic attraction between the metal scale and the metal scale to increase the friction between them. The scale on the surface of the metal scale also increases the friction between them by increasing the roughness, reducing the possibility of the magnet being moved after being driven by the metal pendulum, and increasing the stability of the simple pendulum system.

[0022] 4. Through the swing trajectory calculation method of the magnetic pendulum device and according to the control equation of the magnetic pendulum, the relationship between the magnetic pendulum angle and the light intensity and magnetic field intensity can be obtained. Taking the light intensity as an example, the greater the light intensity, the greater the swing amplitude of the magnetic pendulum and the smaller the frequency. Therefore, by controlling the light intensity and magnetic field intensity, the swing amplitude and frequency of the magnetic pendulum can be controlled to meet the requirements of different swing amplitudes and frequencies of the magnetic pendulum, making it convenient to apply the magnetic pendulum to different scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] The drawings described herein are used to provide a further understanding of the present application and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings: Figure 1 It is a schematic structural diagram of the present invention as a whole; Figure 2 This is a schematic diagram of the simple pendulum and metal scale of the present invention; Figure 3 is a cross-sectional view of the simple pendulum and the metal scale of the present invention; Figure 4 Schematic diagram of the structure of the crossbar, LCE fiber and metal pendulum of the present invention; Figure 5 Schematic diagram of the structure of the metal scale and bending frame of the present invention; Figure 6 It is a structural schematic diagram of the bending frame of the present invention; Figure 7 The wave line diagram of the single-cycle self-excited oscillation of the magnetic pendulum of the present invention; Figure 8 is the force diagram of the magnetic pendulum of the present invention; Figure 9 This is a model diagram of the magnetic pendulum of the present invention.

[0024] In the figure: 1. Experimental platform; 2. LCE fiber; 3. Metal pendulum; 4. Magnet; 5. Metal scale; 6. Simple pendulum bracket; 61. Base; 62. Metal rod; 63. Cross bar; 64. Threaded rod; 65. Nut; 7. Constant light area; 8. Bolt 1; 9. Bending frame; 10. Limit rod; 11. Bending plate; 12. Spring; 13. Gasket; 14. Bolt 2. DETAILED DESCRIPTION

[0025] The following will describe the implementation methods of the present application in detail with reference to the accompanying drawings and examples, so that the implementation process of how the present application applies technical means to solve technical problems and achieve technical effects can be fully understood and implemented accordingly.

[0026] Example 1 In order to provide a new low-power continuous motion method for the pendulum and reduce the pendulum's dependence on external forces such as electromagnetic force and spring, Figures 1-4As an embodiment of the present invention, a magnetic pendulum device based on liquid crystal elastomer fibers that can sustain self-oscillation is proposed. This device utilizes the flexibility and shape variability of liquid crystal elastomer fibers, allowing them to change shape through temperature variations. The constant illumination area is achieved using infrared light emitted from an 808nm high-power near-infrared laser, or by focusing sunlight through a magnifying glass. A pendulum support 6 is mounted on the top of the experimental platform 1. An LCE fiber 2 is fixedly connected to one side of the pendulum support 6, and a metal pendulum bob 3 is fixedly connected to the end of the LCE fiber 2 furthest from the pendulum support 6. The top of the experimental platform 1... The device is equipped with a metal scale 5, and a magnet 4 is slidably connected to the top of the metal scale 5. After the LCE fiber 2 reaches equilibrium, a constant illumination area 7 is applied at the equilibrium point. In use, a single-domain LCE fiber 2 is first made, and then a pendulum support 6 is built. The metal pendulum 3 moves to the vertical direction under the action of gravity, and then the magnet 4 is moved along the metal scale 5 until the magnet 4 moves to a distance from the center point of the pendulum support 6. At this time, the metal pendulum 3 moves towards the magnet 4 under the influence of the magnetic field of the magnet 4 until the metal pendulum 3 tilts at a certain angle and maintains equilibrium under the action of gravity and the magnetic force of the magnet 4.

[0027] A near-infrared laser is used to illuminate the equilibrium point of LCE fiber 2, forming a constant illumination region 7 at the equilibrium point of the LCE fiber. Under the illumination, LCE fiber 2 contracts, causing the metal pendulum 3 to swing downwards. At the same time, after LCE fiber 2 moves outside the constant illumination region 7, it gradually returns to its initial length. Under the action of its own gravity and the magnetic force of magnet 4, the metal pendulum 3 returns to the equilibrium point. The above process is repeated. The heat from the illumination in the constant region continuously drives the pendulum system to swing continuously with low power consumption. It does not rely on external forces such as electromagnetic force and springs for driving. Instead, it uses the temperature provided by the illumination region to achieve the low-power continuous swing of the pendulum, providing a new method for realizing continuous swing.

[0028] In order to facilitate the adjustment of the height of the pendulum system, refer to Figures 1-4The pendulum support 6 includes a base 61 mounted on the top of the experimental platform 1. A metal rod 62 is fixedly connected to the top of the base 61. A pendulum crossbar 63 is sleeved on the outside of the metal rod 62. A threaded rod 64 is installed on one side of the pendulum crossbar 63. A nut 65 is sleeved on the outside of the threaded rod 64. One end of the LCE fiber 2 is fixed to the threaded rod 64. The distance between the crossbar 63 and the base 61 is greater than the length of the LCE fiber 2. A circular hole adapted to the metal rod 62 is opened on the top of the crossbar 63. A bolt 8 with one end movable to the inside of the circular hole is provided on one side of the crossbar 63. The metal pendulum 3 is a metal ball. A limiting hole penetrating its center is opened on one side of the metal pendulum 3. One end of the LCE fiber 2 is movable through the limiting hole. In use, the crossbar 63 is moved along the metal rod 62 until the distance between the crossbar 63 and the base 61 exceeds the length of the LCE fiber 2. The bolt 8 is rotated into the circular hole, so that the bolt 8 is pressed against the metal rod 62, and the crossbar 63 is fixed on the metal rod 62.

[0029] At this point, one end of the LCE fiber 2 is wrapped and fixed to the threaded rod 64, and the other end of the LCE fiber 2 is passed through the metal pendulum 3 and tied in a knot to prevent the metal pendulum 3 from falling off the LCE fiber 2. The spherical metal pendulum 3 facilitates the measurement of its center of gravity and the length of the pendulum system. At this point, the assembly of the pendulum system is completed. Next, the magnet 4 is moved along the metal scale 5 so that the magnet 4 is kept at a distance from the metal rod 62. Under the combined action of its own weight and the magnetic force of the magnet 4, the metal pendulum 3 swings at a certain angle and maintains balance, causing the LCE fiber 2 to swing simultaneously. Finally, the balance point of the LCE fiber 2 is irradiated with a near-infrared laser. The LCE fiber 2 contracts under light and elongates under non-light conditions. The continuous swing of the pendulum system is achieved by using the light in a fixed area. The height of the pendulum system can be adjusted as needed to meet the requirements of assembling pendulums with LCE fibers 2 of different lengths.

[0030] In order to maintain the balance of the simple pendulum system at a certain angle, refer to Figure 2 The size of the metal pendulum 3 is smaller than that of the magnet 4. The magnet 4 is placed on a metal scale 5 at a distance from the center point of the pendulum bracket 6 to attract the metal pendulum 3. The purpose of placing the magnet 4 is to establish a second stable state in addition to the gravitational field: the magnetic field. One end of the LCE fiber 2 is connected to the metal pendulum 3 and maintains balance under the attraction of gravity and the magnet on the metal pendulum 3.

[0031] Example 2 Since the magnet 4 has a tendency to move upward due to the reaction force of the metal pendulum 3, in order to maintain the stability of the position of the magnet 4 and prevent the magnet 4 from moving along the metal scale 5 after being driven by the metal pendulum 3, refer to Figures 1-6On the basis of Example 1, two bending frames 9 are fixedly connected to the top of the experimental platform 1, and a limit rod 10 is fixedly connected between the bending frame 9 and the experimental platform 1. The outer sleeve of the limit rod 10 is provided with a bending plate 11 for squeezing the metal scale 5 toward the experimental platform 1, and a spring 12 is fixedly connected between the bending plate 11 and the experimental platform 1. The spring 12 is sleeved on the outside of the limit rod 10, and a gasket 13 is fixedly connected to the top of the bending plate 11. The limit rod 10 movably passes through the gasket 13, and a bolt 2 14 is provided on the top of the bending frame 9, one end of which movably passes through the bending frame 9. When in use, in order to reduce the possibility of the magnet 4 being attracted by the metal pendulum 3 and moving upward, the metal scale 5 of the present invention is made of magnetic metal material, and the magnetic attraction between the magnet 4 and the metal scale 5 is utilized, combined with the gravity of the magnet 4 itself, to prevent the magnet 4 from being attracted by the metal pendulum 3 and moving upward.

[0032] Since the metal pendulum 3 exerts a pulling force on the magnet 4 in both the upward and left directions, the squeezing force between the magnet 4 and the metal scale 5 is reduced, thereby reducing the static friction between the magnet 4 and the metal scale 5, making it easier to drive the magnet 4 to move along the metal scale 5. The bent plate 11 is manually moved to above both ends of the metal scale 5, and then the second bolt 14 is turned. The second bolt 14 gradually descends along the bending frame 9, pushing the gasket 13 and the bent plate 11 to gradually descend until the bent plate 11 is pressed against the top of the metal scale 5, squeezing the metal scale 5 and fixing it on the experimental platform 1. This can increase the firmness of the connection between the metal scale 5 and the experimental platform 1 and prevent the magnet 4 from dragging the metal scale 5 along the experimental platform 1. At the same time, the gravity of the magnet 4 itself and the magnetic attraction between it and the metal scale 5 are used to increase the friction between them. The scale on the surface of the metal scale 5 also increases the friction between them by increasing the roughness, reducing the possibility of the magnet 4 being moved after being driven by the metal pendulum 3, thereby increasing the stability of the simple pendulum system.

[0033] Example 3 Reference Figures 1-9 , Figure 7 is the angle between the LCE fiber and the vertical direction in the magnetic pendulum device The wave line diagram changes with time. Based on the first embodiment, a method for calculating the swing trajectory of a magnetic pendulum device based on the self-sustaining swing of liquid crystal elastomer fibers is proposed. For simplicity, we ignore the air damping of the LCE fiber and only consider the air damping of the metal pendulum. Compared with the mass of the metal pendulum, the mass of the LCE fiber is negligible. In the absence of light, the LCE fiber reaches a state of equilibrium at a certain angle under the action of the magnetic force of the magnet. The applied range at this angle is In the illumination interval, the LCE fiber shrinks under the illumination conditions, the balance is broken, and under the action of gravity, it swings downward into the non-illumination interval. The LCE fiber slowly stretches and performs a simple pendulum-like motion in the non-illumination interval. After the LCE fiber recovers its original length, it returns to its initial position under the action of magnetic force, that is, in the illumination interval, and then performs the above-mentioned periodic motion.

[0034] During the exercise, according to Figure 8 The force analysis of the magnetic pendulum can be obtained by the momentum theorem as the control equation: ; here It is the tangential component of the air damping torque. It is the damping coefficient. It's the mass of the ball. It is the length of the LCE fiber. This is the initial length of the LCE fiber. It is the magnetic force exerted by the magnet on the metal pendulum. It is the lever arm of the magnetic force relative to the LCE fiber. Indicates the lighting area. It is gravitational acceleration, and, It is the angle between the LCE fiber and the vertical direction. represent That is, the angular velocity of LCE fibers. It is the oscillation time of the magnetic pendulum. is the magnetic field strength. Equation (6) can be further transformed into: ; Indicates the angular acceleration of LCE fibers , Represents the radial velocity of the metal pendulum. .

[0035] Then, a dimensionless parameter is introduced: , , , , , , , It is the damping coefficient. It is the mass of the metal pendulum. It is the length of the LCE fiber. This is the initial length of the LCE fiber. It is the magnetic force exerted by the magnet on the metal pendulum. It is the lever arm of the magnetic force relative to the LCE fiber. is the acceleration due to gravity, is the swing time of the magnetic pendulum, is the magnetic field strength.

[0036] After defining the dimensionless parameter, equation (7) can be transformed into the following dimensionless equation: Illumination range: ; Non-illuminated areas: ; Based on the control equation of the magnetic pendulum, the relationship between the pendulum angle and the light intensity and magnetic field strength can be obtained. Taking the light intensity as an example, the greater the light intensity, the greater the swing amplitude and the smaller the frequency of the magnetic pendulum. Thus, by controlling the light intensity and magnetic field strength, the swing amplitude and frequency of the magnetic pendulum can be controlled to meet the requirements for different swing amplitudes and frequencies of the magnetic pendulum, making it convenient to apply the magnetic pendulum to different scenarios.

[0037] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A self-sustaining magnetic pendulum device based on liquid crystal elastomer fibers, comprising an experimental platform (1), characterized in that: A pendulum bracket (6) is installed on the top of the experimental platform (1), an LCE fiber (2) is fixedly connected to one side of the pendulum bracket (6), an end of the LCE fiber (2) away from the pendulum bracket (6) is fixedly connected to a metal pendulum (3), a metal scale (5) is installed on the top of the experimental platform (1), a magnet (4) is slidably connected to the top of the metal scale (5), a constant illumination area (7) is applied to the balance of the LCE fiber (2), and the constant illumination area (7) is achieved by using any one of infrared light emitted by an 808nm high-power near-infrared laser and sunlight through a magnifying glass for focusing and heating.

2. The magnetic pendulum device according to claim 1, characterized in that: The pendulum bracket (6) comprises a base (61) mounted on the top of the experimental platform (1); a metal rod (62) is fixedly connected to the top of the base (61); a cross rod (63) is sleeved on the outside of the metal rod (62); a threaded rod (64) is mounted on one side of the cross rod (63); a nut (65) is sleeved on the outside of the threaded rod (64); one end of the LCE fiber (2) is fixed to the threaded rod (64); and the distance between the cross rod (63) and the base (61) is greater than the length of the LCE fiber (2).

3. The magnetic pendulum device according to claim 1, characterized in that: A round hole matching the metal rod (62) is provided at the top of the cross bar (63), and a bolt (8) having one end movably extending into the round hole is provided on one side of the cross bar (63).

4. The magnetic swing device according to claim 1, characterized in that: The metal pendulum (3) is a metal ball. A limiting hole pendulum-penetrating the center of the metal pendulum (3) is provided on one side thereof. One end of the LCE fiber (2) movably penetrates the limiting hole. The size of the metal pendulum (3) is smaller than the size of the magnet (4). The magnet (4) is placed on a metal scale (5) at a distance from the center point of the pendulum bracket (6) to attract the metal pendulum (3).

5. The magnetic pendulum device according to claim 1, characterized in that: The top of the experimental platform (1) is fixedly connected to two bending frames (9), a limit rod (10) is fixedly connected between the bending frame (9) and the experimental platform (1), the outer sleeve of the limit rod (10) is provided with a bending plate (11) for pressing the metal scale (5) toward the experimental platform (1), a spring (12) is fixedly connected between the bending plate (11) and the experimental platform (1), the spring (12) is sleeved on the outside of the limit rod (10), a gasket (13) is fixedly connected to the top of the bending plate (11), the limit rod (10) movably penetrates the gasket (13), and a bolt (14) is provided at one end of the bending frame (9) that movably penetrates the bending frame (9).

6. A method for calculating the swing trajectory of a magnetic swing device according to any one of claims 1 to 5, characterized in that: The following steps are involved: Step 1, establishing a model of the magnetic pendulum device and measuring model parameters; Step 2, calculating the motion period of the simple pendulum according to the model parameters; Step 3, obtaining the first control equation of the magnetic pendulum device according to the momentum theorem; Step 4: Import represents the angular velocity of the LCE fiber , the first control equation is optimized to obtain the second control equation of the magnetic pendulum device, is the angle between the LCE fiber and the vertical direction; Step 5: Calculate the following dimensionless parameters based on the model parameters: ； In the formula, is the damping coefficient, is the mass of the metal pendulum, is the length of the LCE fiber, is the initial length of the LCE fiber, is the magnetic force exerted by the magnet on the metal pendulum. is the force arm of the magnetic force relative to the LCE fiber, is the acceleration due to gravity, is the swing time of the magnetic pendulum, is the magnetic field strength, is the horizontal distance between the metal pendulum and the magnet, which is dimensionless after dedimensionalization , is the contraction coefficient, which is dimensionless. ; Step six, replace the model parameters in the second control equation with dimensionless parameters to obtain the third control equation including both the illuminated interval and the non-illuminated interval.

7. The swing trajectory calculation method according to claim 6, characterized in that: In step three, the expression of the first control equation of the magnetic pendulum device is: ； In the formula, is the tangential component of the air damping torque.

8. The swing trajectory calculation method according to claim 6, characterized in that: In step 4, the expression of the second control equation of the magnetic pendulum device is: ； In the formula, represents the angular acceleration of the LCE fiber , Indicates the radial velocity of the metal pendulum .

9. The swing trajectory calculation method according to claim 6, characterized in that: In step six, the expression of the third control equation in the illumination interval is: ； In the formula, It represents the dimensionless form of the angular velocity of the LCE fiber in the illumination range.

10. The swing trajectory calculation method according to claim 6, characterized in that: In step six, the expression of the third control equation in the non-illuminated interval is: ； In the formula, It represents the dimensionless form of the angular velocity of the LCE fiber in the non-illuminated range.

Images